Machine-learning models for building interatomic potentials rely on a local
mapping of structural features onto a set of descriptors. A robust and versatile
choice that allows for an accurate description of the many-body interactions is
to map the local environment around each atom \(i\)  in a system of \(N_\textup {a}\) 
atoms onto two- and three-body atomic distribution functions [1]}.
In this work we relied on so-called separable descriptors introduced in
Ref. [2]}, with the two- and three-body distribution
functions (\(\rho _i^{(2)}\)  and \(\rho _i^{(3)}\) , respectively) defined as:
\(\rho _i^{(2)}(r) = \:\frac{1}{4\pi } \int \!\!d\hat{{\bf r}}\,\rho _i(r\hat{{\bf r}})\,; \\[4pt]\rho _i^{(3)}(r,s,\theta ) = \int \!\!\!\!\int \!\!d\hat{{\bf r}}d\hat{\mathbf {s}}\:\delta (\hat{{\bf r}}\cdot \hat{\mathbf {s}} -\cos \theta )\times \!\bigg [ \rho _i(r\hat{{\bf r}}) \rho _i^*(s\hat{\mathbf {s}})-\sum _{j\ne i}^{N_{\textup {a}}} \tilde{\rho }_{ij}(r\hat{{\bf r}})\tilde{\rho }^*_{ij}(s\hat{\mathbf {s}}) \bigg ].\) 
